- 01-379 M. Christ and A. Kiselev
- Scattering and wave operators for
one-dimensional Schr\"odinger operators with slowly
decaying nonsmooth potentials
(150K, LaTeX)
Oct 16, 01
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Abstract. We prove existence of modified wave operators for one-dimensional
Schr\"odinger equations
with potential in $L^p(\reals)$, $p<2$. If in addition the potential
is conditionally integrable, then the usual M\"oller wave operators
exist. We also prove asymptotic completeness of these wave operators
for some classes of random potentials, and for almost every boundary
condition for any given potential.
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